Thanks everyone!
@gertsy - I ordered two of those batteries today. Fingers crossed that that's all I need!
@Lozspd4 - Ugh, I hope I don't have that problem! Although I'll admit to leaving the soldering iron on there a bit long, I wanted to make sure it was solid.

On the bright side I ordered two of the AmigaKit battery kits "just in case"(TM), so I have a spare.
@Tenacious - schematics would be great! Do you have them somewhere I could download, or can you email them to me at ******@**********? The only ones I've been able to find online so-far are ones for the A4000, which have been less than helpful. :-/
If the replacement battery doesn't solve the problem it sounds like it's time to pull the board again and check the trace going from the battery to the clock chip. I'm assuming it's just one line somewhere, and once I've identified that I should just be able to measure for 3V at whatever pin on the clock chip, correct? And if I'm getting less than that, or no voltage, and the AmigaKit kit isn't the problem, I can just run a bypass wire? Seems simple enough.

**shakes my fist at the sky in the direction of C= designers who went with these leaky batteries, LOL**